# Efficient Vertex-Label Distance Oracles for Planar Graphs

@article{Mozes2017EfficientVD, title={Efficient Vertex-Label Distance Oracles for Planar Graphs}, author={Shay Mozes and Eyal E. Skop}, journal={Theory of Computing Systems}, year={2017}, volume={62}, pages={419-440} }

We consider distance queries in vertex-labeled planar graphs. For any fixed 0 < π β€β1/2 we show how to preprocess a directed planar graph with vertex labels and arc lengths into a data structure that answers queries of the following form. Given a vertex u and a label Ξ» return a (1 + π)-approximation of the distance from u to its closest vertex with label Ξ». For a directed planar graph with n vertices, such that the ratio of the largest to smallest arc length is bounded by N, the preprocessingβ¦Β Expand

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